Model Reduction for Linear and Nonlinear Gust Loads Analysis

1. Model Reduction for Linear and Nonlinear Gust Loads Analysis A. Da Ronch, N.D. Tantaroudas, S.Timme and K.J. Badcock University of Liverpool, U.K. • AIAA Paper 2013-1942 • Boston, MA, 08 April 2013

2. Mini Process Chain Based on CFD CFD Grids FE Models Shape Optimisation eigenvectors Flutter Calculations + iterations Gust Loads

3. Flutter Calculations • Stability studied from an eigenvalue problem: • Schur Complement formulation: Badcock et al., Progress in Aerospace Sciences; 47(5): 392-423, 2011

5. Badcock, K.J. and Woodgate, M.A., On the Fast Prediction of Transonic Aeroelastic Stability and Limit Cycles, AIAA J 45(6), 2007.

6. Mini Process Chain Based on CFD CFD Grids FE Models Shape Optimisation eigenvectors Flutter Calculations + iterations This Talk Gust Loads

7. Model Reduction

8. Model Reduction Project against left eigenvectors Ψ to obtain differential equations for z Badcock et al., “Transonic Aeroelastic Simulation for Envelope Searches and Uncertainty Analysis”, Progress in Aerospace Sciences; 47(5): 392-423, 2011

9. Model Reduction 2nd/3rdJacobian operators for NROM Da Ronch et al., “Nonlinear Model Reduction for Flexible Aircraft Control Design”, AIAA paper 2012-4404; AIAA Atmospheric Flight Mechanics, 2012

10. Model Reduction control surfaces, gust encounter, speed/altitude Da Ronch et al., “Model Reduction for Linear and Nonlinear Gust Loads Analysis”, AIAA paper 2013-1942; AIAA Structural Dynamics and Materials, 2013

11. CFD Solver Overview • Euler (Inviscid) results shown in this paper • Solvers include RANS also • Implicit Formulation • 2 Spatial Schemes • 2d results  meshless formulation • 3d results  block structured grids • Osher/MUSCL + exact Jacobians • Time domain: Pseudo Time Stepping • Linearised Frequency Domain Solver

12. Gust Representation: Full order method (Baeder et al 1997) • Apply gust in CFD Code to grid velocities only • No modification of gust from interaction • No diffusion of gust from solver • Can represent gusts defined for synthetic atmosphere

13. Precomputed Evaluated in ROM

14. NACA 0012 Aerofoil point cloud Coarse 7974 points Medium 22380 points Fine 88792 points Badcock, K. J. and Woodgate, M. A, AIAA Journal, Vol. 48, No. 6, 2010, pp. 1037–1046

15. Steady state: Mach 0.85; α=1 deg

16. Mach 0.8; Pitch-Plunge “Heavy Case” Flutter Speed Ubar=3.577 Speed for ROM Ubar=2.0 Modes corresponding to pitch/plunge retained for ROM  2 modes; 4 DoF

17. 1-cosine gust: Intensity 1% Gust length 25 semi-chords

18. Peak-Peak very similar Discrepancies in magnitude  enrich basis 1-cosine gust: Intensity 1% Gust length 25 semi-chords

19. Worst Gust Search at M=0.8: 1-cos family Gust Lengths between 1 and 100 chords Kriging Method and Worst Case Sampling: 31 evaluations of ROM Worst Case: 12.4 semi chords (excites pitching mode)

21. Response to Von Karman gust, frequencies to 2.5 Hz

22. Finite Differences for Gust Influence  reduce to virtually zero by analytical evaluation

23. GOLAND WING 400k points 1.72 Hz 3.05 Hz 9.18 Hz 11.10 Hz Mach 0.92

24. Mach 0.85; α=1deg ROM calculated at 405 ft/sec EAS Modes corresponding to normal modes retained  4 modes; 8 DoF

25. 1-cosine gust: Intensity 0.1% Gust length 480 ft

26. Worst Gust Search at M=0.8; 1-cos family Gust Lengths between 5 and 150 chords KrigingMethod, Worst Case Sampling: 20 ROM evaluations Worst Case: 65 chords (excites first bending mode)

27. Conclusions • Model Reduction method formulated • Tests on pitch-plunge, flexible wing case Future RANS Rigid Body DoFs Alleviation